Nonreciprocal wave transmission



July 26, 1960 w. J. .cRowE NONRECIPROCAL WAVE TRANSMISSION Filed Dec. 30, 1957 INVENTOR By W. J. CROWE )1 41 ATTOQNEV FIG. 4

. Howev r in "This invention relates to elect-rornag netic wave transmission systems and, -more ,particularly, t-o tra'nsrnission structures having nonreciprocal attenuating properties for "use in such systems. H p I a The use of ferrite materials having gyrornagnetic propcities to obtain nonreciprpcal eflect sjn-inicrowave transmission circuits "is widely know'rrand has foundnurnerous applications in --the wave :guide transriiission art. These efiects have generally beenexpl ained hy the ielectr pn spin coupling concept whereby {the electron spins in the i-ferrite material cziuple with circtilarlypd'lafized n agnetic niaeompbnems ofa wavepropagated through the 'ferrite inediuin. According to this theory, a region of circular,pol arization-fihust exist in theprbpagated wavea'nd therefore lon g it udinal inagnetic field components must eiist in the 'fieldpattern of the wave. The greater 'pro- ;pb'm n er the mines eapzbie erbein 's'u pbnea in' c'onviitiofial hoitoy'vripi'pe'wa games have such longitudinal components and'accordin gly s'uch fgiiid'es hav'e @nnseu eiten'sively for noniecipibcal microwave c rc iiit chih- Ipo'nents. Hollow pipe 'wa'v'e fg uid'es hewever, have a limited fietiuehe range, the lowest frequency capable of tralismissiohteihg d'etei niined i iiy the diiiiehsiiinsdf hr q v1 t, '{Q :I'j- 1 The mode best suitedandirnost widely meager lower -frequencytiiansinission is esdominaiit me l Dire to "this fact, 'n'o' 'gifeet 'iibiiiieip'rocal stiucturs have been available 5hr frequent fies hel'dv'v flie Jiiirmvave rang umil recently. a V p a ewe cbpendmg tt ipucetf 'iis 'gb jnq Se-idel, serial NP'S. "554,237 554271, both of which were filed on December 20, 1'9 hasbeendisclosed that an ieletric zeenstants in the trainsi'n'iss ion medium sup e nigaipur ely tranev'ers'e magnetic ni'odeof "electromagnetic ave ehefgy'jpeitufbs'the wave "so as fto tend to Iforrn ongitudinakcomponents -(if niag- ,ritic nus; ih'the 'regioh-near 'the iiis'continiiity, Such a diseontinuity exists at "thelfac'es V 'a f frri te slab "located Within a medium of i'e1ativ1 115w dielectric constant.

he bppdsite faces of'ihe'Q-fer- These regionsbr cmar polarizz ltionfhave gheticffluxgwhich. have opo fofe beheved that even though hired Stat s P tC' U Patented July 2e, 1969 types -of asymmetric dielectric" and ferrite loading are quence, the efiectiye :permeabilit-ies and/or ,phase constants are different for opposite directions of propagation, respectively, through the line. 2111 this Way nonreciprocal phase shifters, gyromagnetic resonance -isolators, and resistance sheet; eld-displacement isolators may be ,provided for coaxial-lines. 4 1 p Further analysis in accordance with the present invention, however, has dt nonstrated that the nonre'ciprocal phase constants considered essential in the aboyementioned copending applicationsforall nonreciprocal effects including-anon reciprocal attenuation in a resitancesheet field displacement isolator, is not in f-actga-necessary-condition. This recognition is based uponthe fact thatinonreciprocal field displacement-may exist even in the :presence ofga completely reciprocal tp'hase constant in a :properly designed structure; p Y It is thegprincipal objectof this invention-to provide isolator action in a transmissionline supporting the mode with a structurally simplified fielddisplacement device. t

I -In accordance withthe invehtion, it .hasheen found that Tfield displacementiby antelement exhibiting the gyromagnetic efiect at Wave energy frequencies within a g'iven igange of operating frequencies tis a nonreciproeal effect that: can be produced even though phase-shift produced by the element iis-reciproca'l vand the resonance attenuation that would be produced under like conditions (but with :a mag netic biasing field of properfintensity) would also be reciprocal in operation. Hereinafter, when the term gyroma'gnetic materiahbr medium, is used the mo re completly desciiptive definition above will 'beimplie'd. :This nonreciprocal operation occurs because of a .pushqnill effect eharacter-isticbf gyromagne'ticimateria l relative .to fie l-d displacement that "does not otherwise exist relative tof'ether effects. Consider .a-s'lab of .ferrite extending longitudinally infa coaziial linesuh' 't'hatthef IEM mode therein is, perturbed to r'provide rotafing magnetic field components .Irelative Tito the transverse .magnetic {field itfhejferrife) :rotation' is of opposite sense v opposite'faces offt he slahvasiiiseussed abcive. i 81 ordi glyft'hejriheihilityfi one faceissgreaterihan umty whilefat the "other face itis less than-unity. This results, at brie face, "in thef fer'lite tending' to concentrate the electric field c'ompdneiit's' at that face, i.e., t "2115- fplaeWofipiiH the electric fielilpattern of the radio-fre- "que'ncylwavetowa'rd that face. Biit'the other-iace'ofithe slab, Becausedf the different ipe'rmeahility caused'by the opposite sense V of circular fpol arization, will displace dr hfithej'fe'cti'ic fadio ffe'queney field patter-n away from at'se'lf. 'Biit Lihis 'inefans, inja eo'asiialtine, that the these uncann 'polarized :cbinpbiients may ihteract'with the t face-*oTthe slab. 'Thefacti'o'ns of the apposite races of th abseeep' upmauc the same eiie'ct. For "one; d ection of, tien the first face ffbfuil the iefetr 'ffield "to itself while the. second face "ifipus'hei the electricfieldtromjitselfitowardthe first :Eace. 'ZFor "the os'ite direction 'dfipfrbpagati'qn ever thing is reversed.

V leetfiwfild intensity flier'et. Siifc'e this iiitensity "is 'diiferent for opposite directions of .prgpagation through the *linegtne attenuationtprodueed'hyjthe Jessy material isfndiii eipfojcah t t. v In the preferred embed 'cif'the invention, solely a isingle sectofalfIab 6T g"yr magntic material ma ma; many biased in"m nim senireetfdnwith a'coa'tihg 62 Accordingly, it "either face the field Ld'IspIacement'is. .non

3 Q lossy material disposed solely on one face, is located in the coaxial line. The coaxial line is otherwise filled with a homogeneous dielectric material of low dielectric constant. In this way, nonreciprocal attenuation is provided. However, the most efiicient nonreciprocal attenuator or isolator requires substantially zero loss in the forward direction of propagation which in turn requires more 'than a mere diminution of the intensity vof the electric field pattern-at the lossy material for the forward direction; it requires zero electric field intensity, a complete null. In accordance with the invention, a relationship between the thickness of the ferrite slab and other parameters, of the coaxial line isolator is established to provide such an electric field null.

These and other objects and features of the invention, the nature of the present invention and its various advantages, will appear more fully upon consideration of the accompanying drawings and the following detailed description of these drawings.

In the drawings:

Fig. 1 is a perspective view of the principal embodiment of the invention showing a ferrite slab with a resistive element on one face loading a coaxial line and capable of exhibiting nonreciprocal attenuation;

Fig. 1A is a cross sectional view of the coaxial line isolator of Fig. 1;

Fig. 2, given for the purpose of illustration, is a cross sectional view of an unloaded coaxial line shovw'ng the field configuration of the dominant mode wave in such a line at a particular instant;

Fig. 3, given for the purpose of illustration, is a partial view of the ferrite element in the structure of Fig. 1 showing typical magnetic flux lines in the ferrite element at a particular instant; and

Fig. 4, given for purposes of explanation, is a perspective view of parallel plate wave guiding structure, loaded with a ferrite slab, which is an electrical analog of a coaxial line such as that of Fig. 2.

Referring more particularly to Figs. 1 and 1A, a nonreciprocal attenuator, or isolator, is shown as one illustrative embodiment of the present invention. The nonreciprocal attenuator of Fig. 1 includes a section of coaxial line 10 having two branches represented by aand b and comprising an inner cylindrical conductor 11 anda concentric outer cylindrical conductor 12, separatedby. a

region 13. Region .13 is filled with a homogeneous dielectric material which may include air, polyethylene, or other of the many materials normally used fo i. this purpose. Extending between inner conductor 11 and Element 14 has two oppositely disposed longitudinal faces 32 and 34 and is composed of ferrite materials combined in a manner hereafter described. It may, for example, be a combination of iron oxide and a small amount of one or more metals such as nickels, magnesium, zinc, manganese or aluminum. These materials are characterized by the fact that they exhibit gyromagnetic properties at microwave frequencies and can, therefore, be spoken of as gyromagnetic materials. example, elements 14 and '15 may be made of magnesium-manganese-aluminum ferrite prepared in the manner described by C. L. Hogan inhis United States Patent No. 2,748,353, which issued May 29 1956. Element 14 may be provided with wedge-like tapers at'both ends, to prevent undue reflections of wave energy-therefrom.

I Element 14 is biased by a steady magnetic field so as to be polarized at right angles to the axis" of guide 10. As shown inFig. 1, thispolarizing field may be supplied by a solenoid structure comprising magnetic core 19 having ftwo pole-pieces 2 0 and 2 1 displaced around the periphery As a specific of and extending longitudinally along guide 10 in the region of element 14. Turns of wire 22 are so wound on core 19 and connected to source of potential 23 that they produce a north magnetic pole N at pole-piece 21 and a south magnetic pole S at pole-piece 20. The magnetic field produced by this solenoid therefore extends from pole-piece 21 through element 14 in a direction from outer conductor 12 to inner conductor 11 and back to pole-piece 20, thus radially polarizing element 14. This field may be supplied by any other means which will produce the desired direction of polarization in element 14. The field may, for example, be supplied by other configurations of magnetic cores in an electrical solenoid, by an electrical solenoid Without a magnetic core, by a permanently magnetized core, or by permanently magnetizing element 14 itself.

In Fig. 1, the strength of the magnetic field in element 14 can be varied by means of variable resistor 24 connected in series with source of potential 23. The strength of this field is adjusted to a value outside the region of gyromagnetic resonance for element 14 in the operating frequency band.

Resistive sheet 17 is attached to element 14 on face 32 and extends longitudinally along element 14. Sheet 17 is composed of any material which has a high rate of dissipation of electrical energy. For example, sheet 17 may be composed of polyethylene loaded with carbon particles, or it may be a resistive film sprayed on element 14. It will be shown that for the direction of propagation into the plane of the paper a field distribution will result such as that of curve 41 in Fig. 1A. As a consequence, there will be substantially no electric field vectors parallel to sheet 17 and the wave will be substantially unattenuated. However, for the direction of propagation out of the plane of the paper corresponding to the field distribution represented by curve 42, substantial electric field intensity vectors will exist parallel to sheet 17. These electrical field vectors will induce radial currents in sheet 17 which will be dissipated by its resistive properties. How this non-reciprocal field distribution occurs will now be'explained.

An understanding of the present invention can be more readily obtained by an understanding of the gyromagnetic properties of ferrite materials at microwave frequencies.

:One physical explanation which has been advanced to explain these properties is the so-called spin coupling" theory. According to this theory, unpaired electron spins in ferrite materials tend to align their axes of spin with an externally applied magnetic field. The individual spinning electrons have an angular momentum associated with their mass and a magnetic moment associated with their charge. The alignment of these magnetic moments is the phenomenon which gives rise to the classical magnetic properties of ferrous materials. If the spin axes of the electrons are momentarily deflected from alignment with the externally applied field, they will not immediately realign themselves, but will precess about the line of the externally applied field much like a gyroscope. This precession of the unpaired electron spins tends to be in a clockwise sense when looking along the line. of the applied field in the direction of this field.

When the deflection from alignment with the applied field is caused by .a periodically varying magnetic field transverse to the line of the applied field, the resulting precession of the magnetic moment of the electron spins will be circular or elliptical and will produce components of magnetic flux which are circularly or elliptically polarized. .Such a periodically. varying magnetic field exists as part of a transversely propagated electromagnetic of this circular p'olari'zatiori Twith 9t el ment .14 f E ecan be; made nonrecipro'cf" having circularly 1 561 'z'e iyhwhhavehppo sit fidsit'efdlrec tioris of propagation. fiAccor ingjto ithisithebry, there fore, the conditions of nonreiciprocity forla transmitted electromagnetic wave 'arecomponents 'of circularly polar ized magnetic: flair, and'a reversal "in' 'thenghlarse'nste a reversal in the direction: ofpropag'ation. :That'the applicants structuresatie fies theserequirernents can be readily seen by considering Figs. 2 and 3",:gi-i'lh for the purposes or illustration.

In Fig. 2 is shown across sectional View of a coaxial line, much like line 1!} ofFigs. l and 1A comprising an inner cylindrical conductor u'd'a' concentric outer cylindrical conductor 12 sep a by a region 13 filled with a suitable dielectric material. Within region 13 at Fig; 2 is sire-W51 the newscaster-anon "of the new: nant mode wave in such a coaxial line at a particular instant of time; It should be noted that both the 7 electric field lines and the magnetic ;field lines are entirely transverse to the directions of propagation of electr'orngafietic Waves'in r 'e 'cda'xial line, these directions of propagation bein {re resented By "conventi nal notation at circles 26 and 27 as ""ntoor outbfjthe plane of the paper. Furthermore, the electric field liiies, represented by the solid lines in Fig. 2,, ,are radial lines extending between conductors 11 arid 12, and the magnetic field lines, represented by the dashed lines of Fig. 2, form concentric circular loops around inner conductor The arrows on the individual electric and magnetic field lines represent their directioh-nt the particular instant. It should be furthe'rfnotedjthat the L'lectrornagnetic field of the coaxial line is uniformly distributed throughout region 13. With these facts in mind, Fig. 3 may now be considered.

In Fig. 3 is showinfhrthe puhpi'lse of illustration, part in s ntendin serr erae i s portion of inner conductor 11. 'Also shown aremagnetic flux lines 28, representing'portions of certain otthe magnetic ,fi m p at. t s-d n ga sq retai line of'Fig. l at a particular ihstant. "Flux lines 28 rpreen .d storts .r as it n s s i i se sile a aw e919? eane .8, e re entin flux at the particular instau w a J H ep es n the rsq qn QFPL i ti haiwfitei some ba ne t attthei i esti ns .12 etion of the magnetic flux reverses each Half wafvelength. EM:

Assuming that the dielectric constant of element 14 in Fig. 3 is substantially greater than the dielectric constants of the surrounding medium, ;;the' electromagnetic V slowly wave is perturbed that, the wave will travel more in element 14 than in the surrounding media. Ferrite materials.'of the type icontemplate'd have a dielectric c.611-

stant on'the order "of ten'towfifteen while thesurroundin'g I medium inayffor example, 'ber'air with afdielectric eons'tant of substantially unity, or polyethylene with'ard'ielectric constant *ofnbout 2:25 Thus fromra simplified viewpoint, the portions of flux lines 28 "in- 'elemcnt. 14 appear 'tomediu r'n'. Since these fiux-lines.-rmi'stbe' continuous fully closedfloop's, longitudinal fluxvcbmponents ai-el'set -'up "in the regions near the, vsiallsofilemnt '14. Now

consider points 30 and 31 on opposite facesfilran'd ii t, refspectiv'ly, 'of'eler'rient 14. As the wave propagates to *the direction of 1 t'irr'ow?2'9, poiht 30 i is "cono'rnpone'nts of magnetic :fiurr which iifcrentidir'ctions er polarization ieach suce I lag behind the portidns in the surr'ountling is iapparent that a Wave traveling ffohi 6f Fig. lA"'(cu'r Ves 41 and 42 represent 45 race '34 'of elnie'iit 14. With e1 eat; that the irst nts- 'in element -1 4- weui'd lag ts the u direction 'aiid th s se (if circ 'lllal polarization at 3Q arid-31 would lie reversed, rilrrlly, lai'i would lb"6'O1il1f1CldCl WiSe tit point silj'iindl' clckvfs 51731. I

Returning again to Figs. 1 and 1A, fron'rjt b oif' lni'e 10 ould present a clockwise c component er fiuX n ar his. Furthermore, such a wave would presen' wise circularl polarized cdnipone e a steadjin'agnet'ic new as Before lidicated, if directisn Ham 'outer cohduc'to'r '12 thinner u v 11, the angular sense of the precessing electron spin Within the ferrite inat' iiig *r em above. 'It can be seen that for a have prspa a ngrrom "bran 'h iz to branch b, the an ular sense of the eflec'tro nspih precession andthe angular sense hi? the polarized flux be the same at fa'ce 32 "and 5pposweet face '34. The Wave 'Will enceainer, ther e, in are ferrite region at face 32 a magnetic permeability of less than unity, due to this agreement in directions of polarizations. 'jO'nth'e other hand, 'a permeability greater than unit will be encountered at the region of ass 34 due to the 'opposing polarizations. a coils qu ce, Pfae 32 ivill't'efid'to displace electric intensity in of the wave awa from itself so as to concentrate in the su'rrouiliding regions only a smanamouin inthereg'io'n near fade 32. QEileC'tiVl'Y, then, the field "Willlie displaced away horn race 32. Face 34 ofthe ferrite sets dooperatiyelyfto runne hisf fie ct since the permeability "that th'ehivave 'will encblinter at face, is reater than unity, the lcti'ieintensity lir ies affected th'e'rby vvill tetra toco centitatein the region offfacefl i with only a man "amount "in the sufrouhdirl'g r gi oiis'. eifOt Gf the two fa'ces providing perrnabilitis respectively lower and greater than unity "is to Eoope'ra tively. displace the elec c lines er force in 't'lfe sarn'e aljs'o'liite dir'ect'idn." the er ct a field iilteris'ify df th Hi0 I u i the othefface 32 of liern efrit 14in ofb-"a's ihhicated by solid line the direction ream of electric field intensity within the agin the peripher" "of inner "cridiictor 11 as abscissa, fand i'ria'te's').

agrenieritfatface '34. The Waveftl'ierefore, traveling in this direction will encounter pe rfrieabilities t non. The new richer permeabilit Will he di ifereiit; therefb site directions of propagation, and hence "ii nr'eciproc al. lliis'hieans that faces 32 and 34 Willcodperatenow to displace the electric field components of'the 'radio -fre guency wave in the opposite sense fiom which it displaced them in a Wave traveling in. the a to b direction. The electric field intensity distributionfor the b to a direction is, thereforerepresented by broken line curve '42; In the plane of resistive noted that'theelectric field intensity for the direction of propagation from'a to b is zero while in the derecti'on froin b to *a it a "substantial amount. Accordingly, wave energy propagating from a to b wvill supply *rio attenuationwhile for the reverse direction 'of propaga tiorrthe wave energy will be substantially completely "attenuated. e

It has above been demonstrated that the structure of the invention Will provide a"diiiere'ritial in the elfdtiie field intensity distribution at the lossy element, To enthat is, if the were travels rn a iir ection opposite to 7 5 site that an electric new null appease the lossy elee rial will hefclockwise yihen rear,

' solute'tialues nowa was pr pa stin'gnem hrai'ich b enew "to element 17, it inay thereforebe 4 to proportion certain parameters of the embodiment of the Fig. 1 according to' a special relationship. Ifithis is done, substantially zero loss is obtained in one'direce tion of propagation (while a large loss occurs for the opposite direction of progagation); and efficient isolator action is achieved. 7

To develop this parametric relationship, the ferrite slab loaded coaxial line may be viewed as a parallel plate transmission line, as in Fig. 4, to render the mathematical synthesis reasonably manageable. The compatibility and similarity of these two structures for these purposes is well known in the art, and is discussed in detail in' such standard works in the microwave art as Principles and Applications of Waveguide'Tr'ansmission, by G. C. Southworth, D. Van Nostrand Co., Inc, 1950, at pages 93 and 96. Thus, if the two parallel plates of Fig. 4 were bent into concentric cylinders, they would be coaxial in the same way as conductors 11 and 12 of Fig. 2, and separated by a space (as 13 in Fig. 2) if the plates are of different transverse widths in the x direction. However, as Southworth indicates, the error introduced into various calculations of interest by treating the parallel plates as if of equal width is ordinarily small. In this arrangement the transverseelectric field components, which extended radially in the coaxial line, will now extend vertically, while the transverse magnetic components, which extended circularly and concentrically in the coaxial line, will now extend horizontally. In Fig. 4, the ferrite slab at the left-hand of the parallel plate guide is the analog of the sectoral ferrite slab of the coaxial line. As indicated, the left-hand face of the slab corresponds to a position x=0, the right-hand face, or thickness of the slab, to x=6, and the right-hand end, or width, of the parallel plates to x=L. In a coaxial line, 6 is the thickness of the sectoral ferrite slab measured along the arc of a circle concentric to and midway between, the outer surface of the inner-conductor and the inner surface of theouter conductor, while L is the circumference of that same circle. Y I It may be noted that when the plates are bent to form a coaxial line, x= and x=L describe the same point. In

the discussion to follow,,all fieldcomponent parameters so indicated by a superscript within the ferrite slab are while those in the air or dielectric medium are indicated byasuperscript a'. j V V,

A relationship which provides an electric field null at x=0, must not only be one such that the vertical electric field component, E is zero thereat, but must also be compatible with the required boundary conditions for a wave transmission line. Thus E must equal E at x=6; similarly the longitudinal magnetic intensity field component in the ferrite in the y direction, h at x=0 must equal h at x=L; in addition at x=6 it must also be the case that h =h relationship satisfying all possible to establish an electric field null at the face of the ferrite slab.

The first condition is that there be an electric field null at x=0, and x=L and thus would provide such a null, where A and Bare the plitudes of the electric field intensity distributions in If it is possible to develop a the these conditions, then it is ferrite and air. regions, respectively, while transverse phase constants k and k are the rate of change of the electric field intensities respectively. Performing the operations rite, respectively.

From Maxwells equations it may be demonstrated that ft is the phase-constant of the transmisp and 0 are merely shorthand notations In (5) and (6), sion path, while respectively; xxx and xxy are the diagonal and off diagonal components of the magnetic susceptibility tensor, From the prior discussion, the following necessary conditions were established:

and

Ea izz lp-fi By operating on (5) and (6) as indicated by (7) and (8), we obtain respectively,

Ak,,, =-Bk 10 A sin k =1; sin k (L-a) 11) By operating on Equations 1 and 2 as indicated in 9 we obtain.

Thus Equations 10, 11, and 12 incorporate all the necessary conditions for an operative structure with an electric field null at one fact of the ferrite slab, i.e., they incorporate Equations 1, 2, 7, 8, and 9.

Substituting Equations '10 into 11 and 12 and then performing 'various simplifying algebraic and trigonometric operations provides:

' 2 z z z 20-5) cot k 6= (13) null will appear elsewhere in the transmission line than at x=0 (and in particular at x=6). Since the resistive material is located solely at x=0 in the coaxial line, it is clear 'that an efficient isolator is provided by this, parametric relationship.

It is to be understood that the above-described arrangements' are illustrativeof the application of the principles of the invention and no attempt has been made to exhaustively illustrate all possible embodiments thereof. Numerous other arrangements, obviously, may readily be devised by those skilled in the art without departing from the spirit and scope of'the invention. a

What is claimed is: r V L l. A coaxial transmission line for electromagnetic wave energy adapted to propagate said waves within a given frequency range of interest and having a longitudinal axis,

means for exciting said line in a wave mode having magnetic fieldcomponents extending solely circumferentially around the inner conductor of said coaxial line, means disposed within said line for producing an electric field intensity difierential in at least one portion of said coaxial line for wave energy being transmitted in opposite directions of propagation therealong, said means consisting solely of a single element of magnetic material exhibiting the gyromagnetic effect at frequencies within said given range, said element being magnetically polarized in a direction transverse to said direction of propagation and occupying a part only of the transverse cross section of said line, means including a loss producing coating of material of electrical characteristic diiferent from that of said magnetically polarized material located in said one portion for converting said field intensity differential into a nonreciprocal attenuation, and a homogeneous nonmagnetic dielectric material filling the remainder of said cross section.

2. A transmission line as recited in claim 1 in which said element of magnetic material is in the form of a sector-shaped slab extending longitudinally parallel to said axis and having two planar surfaces which extend radially in transverse cross section, one of said surfaces extending within said one portion, said loss producing coating being 25 contiguous to said one surface.

V ,3. A transmission line as recited in claim 2 having proportions'and characteristics satisfying the expression cotangent k 6= References Cited in the file of this patent UNITED STATES PATENTS Shockley Jan. 15, 1957 2,834,947 Weisbaum May 13, 1958 2,849,683 Miller Aug. 26, 1958 OTHER REFERENCES Seidel: Journal of Applied Physics, vol. 28, No. 2, February 1957, pages 218-226, 

